In electrical propulsion machines energy is wasted in various ways including friction, winding resistance and eddy currents. Such losses can be minimized by careful design of the mechanical aspects of the machine and by correct choice of constructional materials. There is however another defect which is related more to the nature of the electrical effects by which the machine operates, especially when at very high speeds. This defect is identified with a quantity called the power factor. The current and voltage in the machine are moved out of phase with one another resulting in an "imaginary" or reactive power component of the electrical energy involved. This reactive component cannot produce a useful output from the machine so it reduces the "real" power available in the machine, reducing the efficiency of both the machine and the associated electrical transmission path and increasing the construction and operating costs of both.
Despite these disadvantages the simple, robust construction of linear induction machines (LIM) has led to their widespread use as main propulsion drives with the acceptance of this cost penalty. Clearly with increasing material and manufacturing costs this penalty is less acceptable.
Induction motors are generally cylindrical and symmetrical but linear motors have a flat geometry for both stator and moving members termed primary and secondary respectively. Such machines have an "open magnetic circuit". The partial stator introduces asymmetry into the electrical and magnetic states which is distinct from the symmetry of a conventional cylindrical induction machine. A conventional linear induction motor has a lagging power factor with a stator current pattern travelling at synchronous speed and induces (printed) in the rotor an identical pattern also travelling at synchronous speed but displaced in the direction of motion in dependence on the ratio of load current to magnetizing current. (This ratio is the magnetic Reynolds number or "Goodness Factor" of the machine and should be as high as possible.)
In the paper "The Asynchronous Condenser: A Brushless Adjustable Power Factor Induction Machine", IEEE Transactions of Power Apparatus, Vol. PAS-99, pp. 2242-2432, 1980, E. R. Laithwaite and S. B. Kuznetsov show the occurrence of a second induced current pattern in the secondary due to transients on the entry of unmagnetized secondary conductive material under the leading edge of the stator and identical to the stator current pattern but travelling at vehicle speed. FIG. 1, which is similar to FIG. 1 of the first of the above references, illustrates the analysis on p. 2242 of this reference. FIG. 1 is a plot of flux in the electromagnetic airgap against distance denoted "s" along the gap normalized as radians in terms of pole pitch and slip to be independent of any particular machine condition. The flux level marked ECM or 2 is that of the steady-state in-phase flux of an "equivalent conventional machine". The two flux components drift in and out of phase during movement of the secondary conductor producing the Bp label 4 and Bq label 6 curves shown in FIG. 1. It should be emphasized that these curves relate to a perfect machine, i.e. one requiring zero magnetizing currents and having zero magnetic leakage. The area under the Bp curve is a measure of the useful power output of the machine as a motor.
The maximum machine efficiency occurs at s/p=.pi. on the distance axis where s=distance along stator-longitudinal and p=pole-pitch. The area quadrants I and IV between Bp and ECM labeled 8 and 10, respectively, represents a reduction in electrical real-power losses in comparison with a conventional machine. The maximum terminal power factor occurs at a slip times distance product of 2 .pi. and based on the equal graph areas on either side of the axis appears to be unity. (The ECM level of Bq is zero, i.e. the distance axis.)
Prior to the slip-distance product reaching 2 .pi. the airgap reactive power which is the integral of the Bq waveform is always lagging and at 2 .pi. the air gap reactive power is zero, and consequently, the power factor is unity. The second current pattern leads to higher secondary conductor losses than in a cylindrical machine, indicated by the area above the Bp curve but below ECM. Also on exit from the stator "back thrust" arises when the magnetized reaction rail on the maglev guideway continues to move from beneath the final energized stator blocks, again leading to transients which result in further losses. This is termed "exit-edge" loss in an uncompensated linear motor. In particular a "perfect" LIM, i.e. having no leakage flux and drawing no magnetizing current would still draw reactive volt amperes from the supply whenever the region between the Bq curve and the axis has more positive area than negative area, resulting in lower, i.e. poorer, power factor.
Reactive power, Q, is the product of the apparent power, s, with the sine of the phase angle .theta.. The amount of real power, p, is indicated by the mathematical product of the power factor (expressed as cos .theta.) and the apparent powers or kVA input. ##EQU1##
This power factor is unity when reactive power is not being drawn. When reactive power is drawn the power factor is less than unity. The higher the proportion of reactive power the lower the power factor. Inductive loads, typically induction motors, have a lagging power factor between 1.0 and zero while capacitive loads, which are rare, have a leading power factor between 1.0 and zero and can offset inductive loads on a common supply. Accordingly the LIM, and open magnetic machines in general, are at a disadvantage, apart from applications where other properties outweigh this poor power factor disadvantage.
Reference has been made to stator and reaction rails above but as the terms are not always clearly identifiable with machine parts the terms primary and secondary will be used respectively to identify that machine part connected to a power supply and that part coupled to the primary by electromagnetic effects. Where the term "winding" is used this includes a solid electrical element of the type found in some linear motors. The term machine extends to both generators and motors.